Wednesday, July 31, 2013

Wednesday: Fucking chi^2 contours

Hopefully ^ is a valid character in titles.

I have 99% of the problem resolved, but it bothers me that I can't get the last bit to work out.  I'm sure that there's still an issue.  I just spent an hour working on it instead of finishing that last sentence, and it's still not totally clear.  I'm beginning to suspect two causes.  One, my Levenberg-Marquardt step may be going wonky.  I'm thinking that maybe saturating lambda may be the right solution, but I'd like to have a better handle than "that's too big."  Second, I seem to be using a delta chi^2 threshold as my stopping criterion, and that may be too lazy.  Delta(parameter vector) is probably a stronger method, or even just taking the norm of the update vector.  Both of these boil down to "I think it's getting lazy at fitting," which isn't good.  Part of the problem is that the aforementioned "fucking chi^2 contours" basically form a hyperbolic trough in parameter space.  Maybe it'd be best to fit for inverse Y to eliminate that issue?



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